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Journals / Sinop Üniversitesi Fen Bilimleri Dergisi / 2025 / Cilt: 10 Sayı: 2

The Infinitude of the Primes via the Hales-Jewett Theorem

Hales-Jewett Teoremi ile Asalların Sonsuzluğu

Azem Berivan Adıbelli(Umeå University)0009-0005-7995-1769
Sadık Eyidoğan(ÇUKUROVA ÜNİVERSİTESİ)0000-0003-4324-9845
Pages
439–449
Publication Date
2025-12-24
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In this way, we demonstrate that primes can be studied not only through classical arithmetic methods but also within broader structural frameworks.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We take a different approach to prove the infinitude of the prime numbers by utilizing the Hales–Jewett Theorem.
📊
Key Findings & Data:This method allows us to examine the distribution of primes while observing how they are situated within specific combinatorial structures.
💡
Conclusion & Impact:In this way, we demonstrate that primes can be studied not only through classical arithmetic methods but also within broader structural frameworks.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Asalların sonsuzluğu · Hales-Jewett Teoremi · Ramsey teorisi

Abstract

We take a different approach to prove the infinitude of the prime numbers by utilizing the Hales–Jewett Theorem. This method allows us to examine the distribution of primes while observing how they are situated within specific combinatorial structures. In this way, we demonstrate that primes can be studied not only through classical arithmetic methods but also within broader structural frameworks.

Özet

Bu çalışmada, asal sayıların sonsuzluğunu kanıtlamak için Hales–Jewett Teoremi kullanılarak farklı bir yol izlenmektedir. Bu yaklaşım, asal sayıların dağılımını incelerken, onların belirli kombinatoriyel yapılar içinde nasıl yer aldığını ortaya koyar. Böylece asal sayıların yalnızca klasik aritmetik yöntemlerle değil, aynı zamanda daha geniş yapısal çerçeveler içinde de ele alınabileceği gösterilmiş olur.

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Cite This Article

Adıbelli, A. B., Eyidoğan, S. (2025). The Infinitude of the Primes via the Hales-Jewett Theorem. Sinop Üniversitesi Fen Bilimleri Dergisi, Cilt: 10 Sayı: 2, 439–449. https://doi.org/10.33484/sinopfbd.1643702

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